nThe extreme "sensitivity to initial
conditions" mathematically present in the systems studied by Poincaré has come to be called
dynamical instability, or simply chaos.
nin a chaotic system, using the laws of physics to make
precise long-term
predictions is impossible, even in theory. Making long-term predictions to any degree of precision at all would
require giving the initial
conditions to infinite precision.
nThe mathematics inside Lorenz's model of atmospheric
currents was widely
studied in the 1970's. Gradually it came to be known that even the smallest imaginable discrepancy between two sets of
initial conditions would always
result in a huge discrepancy at later or earlier times, the hallmark of a chaotic system, of course.
nthe weather as a whole is a chaotic system This means
that in order to make
long-term weather forecasts with any degree of accuracy at all, it would be necessary to take an infinite number of
measurements